Solution for Approaching Quantum Computing 1st Edition Chapter 5, Problem 1

by Dan C. Marinescu Gabriela M. Marinescu
70 Solutions 6 Chapters 9440 Studied ISBN: 9780131452244 Electrical Engineering 5 (1)

Chapter 5, Problem 1 : 5.1 Show that if f(0)  f(1), then...

5.1 Show that if f(0) f(1), then the output of the black box in Deutsch's problem is

Figure 5: The quantum circuit for solving Deutsch's Problem includes a f-controlledNOTcircuit.

Step-By-Step Solution

5.1 Solution: The circuit for Deutsch's algorithm in Figure 5 consists of three stages. The input state vectors for the first two stages are:


The input vector for the third stage is the tensor product of the control qubit, I    x) and the output of the f-controlledNOT circuit, y EB f(x)):

The last expression can be written as:


When f ( 0) =I f ( 1) the expression f ( 0) EB f ( 1) is always equal to 1.  In this case the term

[I 0) + (-l)f(O)EBJ(l) 11)] becomes [I 0)- 11)].


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